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Tian yuan shu

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However, after the Ming overthrew the Mongol Yuan, Zhu and Li's mathematical works went into disuse as the Ming literati became suspicious of knowledge imported from Mongol Yuan times.
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of the unknown by adding more lines on top and negative exponents by adding lines below the constant term. Decimals can also be represented.
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In later writings of Li Zhi and Zhu Shijie, the line order was reversed so that the first line is the lowest exponent.
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means "method of the heavenly element" or "technique of the celestial unknown". The "heavenly element" is the unknown
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Only recently, with the advent of modern mathematics in China, has the tianyuanshu been re-deciphered.
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equations. Some of the earliest existing writings were created in the 13th century during the
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Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences
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was deciphered and was important in the development of
259:) term. The system accommodates arbitrarily high 101:The Tianyuanshu was explained in the writings of 322:but its sources remain unclear because it lacks 121:), two Chinese mathematicians during the Mongol 547: 490: 219: 8: 425:. Vol. 1. JHU Press. pp. 105–106. 554: 540: 497: 483: 373: 353:Learn how and when to remove this message 419:"Indigenous Japanese mathematics, Wasan" 366: 241:. The line below is the constant term ( 45:Jottings on the Science of the Chinese 138:arrived in Japan, where it is called 7: 508: 506: 451: 449: 234:, so the numerals on that line mean 421:. In Ivor Grattan-Guinness (ed.). 158:) in the 17th and 18th centuries. 14: 510: 453: 393:A History of Chinese Mathematics 299: 211: 205: 108:Jade Mirror of the Four Unknowns 390:Martzloff, Jean-Claude (2006). 210:, which in Arabic numerals is 77: 68: 60: 1: 182:It is a positional system of 593:History of mathematics stubs 526:. You can help Knowledge by 469:. You can help Knowledge by 245:) and the line above is the 39:The technique described in 614: 588:13th-century Chinese books 505: 448: 220: 81:) is a Chinese system of 16:Chinese system of algebra 417:Murata, Tamotsu (2003). 308:This article includes a 461:This article about the 337:more precise citations. 522:-related article is a 463:history of mathematics 228:) denotes the unknown 47: 32: 38: 26:in Zhu Shijie's text 22: 578:Japanese mathematics 188:polynomial equations 179:in modern notation. 152:Japanese mathematics 573:Chinese mathematics 65:traditional Chinese 310:list of references 202:is represented as 173:, usually written 57:simplified Chinese 48: 33: 535: 534: 478: 477: 363: 362: 355: 605: 598:Polynomial stubs 556: 549: 542: 514: 507: 499: 492: 485: 457: 450: 442: 440: 439: 413: 411: 410: 377: 374:Martzloff (2006) 371: 358: 351: 347: 344: 338: 333:this article by 324:inline citations 303: 302: 295: 258: 244: 240: 233: 223: 222: 215: 209: 201: 178: 79: 70: 62: 613: 612: 608: 607: 606: 604: 603: 602: 563: 562: 561: 560: 504: 503: 446: 437: 435: 433: 416: 408: 406: 404: 389: 386: 381: 380: 372: 368: 359: 348: 342: 339: 328: 314:related reading 304: 300: 293: 272: 254: 242: 235: 229: 191: 190:. For example, 174: 164: 99: 41:Alexander Wylie 17: 12: 11: 5: 611: 609: 601: 600: 595: 590: 585: 580: 575: 565: 564: 559: 558: 551: 544: 536: 533: 532: 515: 502: 501: 494: 487: 479: 476: 475: 458: 444: 443: 431: 414: 402: 385: 382: 379: 378: 365: 364: 361: 360: 318:external links 307: 305: 298: 292: 289: 288: 287: 284:Ceyuan haijing 280: 271: 268: 163: 160: 147:Suanxue qimeng 118:Ceyuan haijing 98: 95: 29:Suanxue qimeng 15: 13: 10: 9: 6: 4: 3: 2: 610: 599: 596: 594: 591: 589: 586: 584: 581: 579: 576: 574: 571: 570: 568: 557: 552: 550: 545: 543: 538: 537: 531: 529: 525: 521: 516: 513: 509: 500: 495: 493: 488: 486: 481: 480: 474: 472: 468: 464: 459: 456: 452: 447: 434: 432:0-8018-7396-7 428: 424: 420: 415: 405: 403:3-540-33782-2 399: 395: 394: 388: 387: 383: 376:, p. 259 375: 370: 367: 357: 354: 346: 336: 332: 326: 325: 319: 315: 311: 306: 297: 296: 290: 286: 285: 281: 279: 278: 274: 273: 269: 267: 264: 262: 257: 252: 248: 239: 232: 227: 216: 214: 208: 203: 199: 195: 189: 186:to represent 185: 180: 177: 172: 168: 167:Tian yuan shu 161: 159: 157: 153: 149: 148: 144:. Zhu's text 143: 142: 137: 136:tian yuan shu 132: 129: 126: 124: 120: 119: 114: 110: 109: 104: 96: 94: 92: 88: 84: 80: 78:tiān yuán shù 74: 66: 58: 54: 53: 52:Tian yuan shu 46: 42: 37: 31: 30: 25: 24:Tian yuan shu 21: 528:expanding it 517: 471:expanding it 460: 445: 436:. Retrieved 422: 407:. Retrieved 392: 384:Bibliography 369: 349: 340: 329:Please help 321: 282: 277:Yigu yanduan 275: 265: 255: 237: 230: 225: 217: 204: 197: 193: 184:rod numerals 181: 175: 166: 165: 155: 145: 141:tengen-jutsu 140: 139: 135: 133: 130: 127: 123:Yuan dynasty 116: 106: 100: 91:Yuan dynasty 76: 51: 50: 49: 44: 27: 23: 583:Polynomials 335:introducing 247:coefficient 162:Description 134:Meanwhile, 567:Categories 520:polynomial 438:2009-12-28 409:2009-12-28 343:March 2023 291:References 103:Zhu Shijie 87:polynomial 261:exponents 251:quadratic 200:− 316 = 0 270:See also 171:variable 331:improve 249:of the 97:History 83:algebra 429:  400:  113:Li Zhi 111:) and 75:: 73:pinyin 67:: 59:: 518:This 465:is a 316:, or 156:wasan 524:stub 467:stub 427:ISBN 398:ISBN 243:-316 226:yuan 218:The 196:+ 18 85:for 125:. 69:天元術 61:天元术 43:'s 569:: 320:, 312:, 236:18 71:; 63:; 555:e 548:t 541:v 530:. 498:e 491:t 484:v 473:. 441:. 412:. 356:) 350:( 345:) 341:( 327:. 256:x 253:( 238:x 231:x 224:( 221:元 198:x 194:x 192:2 176:x 154:( 115:( 105:( 55:(

Index


Suanxue qimeng

Alexander Wylie
simplified Chinese
traditional Chinese
pinyin
algebra
polynomial
Yuan dynasty
Zhu Shijie
Jade Mirror of the Four Unknowns
Li Zhi
Ceyuan haijing
Yuan dynasty
Suanxue qimeng
Japanese mathematics
variable
rod numerals
polynomial equations


coefficient
quadratic
exponents
Yigu yanduan
Ceyuan haijing
list of references
related reading
external links

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